A quantum jump description for the non-Markovian dynamics of the spin-boson model

We derive a time-convolutionless master equation for the spin-boson model in the weak coupling limit. The temporarily negative decay rates in the master equation indicate short time memory effects in the dynamics which is explicitly revealed when the dynamics is studied using the non-Markovian jump description. The approach gives new insight into the memory effects influencing the spin dynamics and demonstrates, how for the spin-boson model the the co-operative action of different channels complicates the detection of memory effects in the dynamics.Comment: 9 pages, 6 figures, submitted to Proceedings of CEWQO200

Test aspects of the JPL Viterbi decoder

The generation of test vectors and design-for-test aspects of the Jet Propulsion Laboratory (JPL) Very Large Scale Integration (VLSI) Viterbi decoder chip is discussed. Each processor integrated circuit (IC) contains over 20,000 gates. To achieve a high degree of testability, a scan architecture is employed. The logic has been partitioned so that very few test vectors are required to test the entire chip. In addition, since several blocks of logic are replicated numerous times on this chip, test vectors need only be generated for each block, rather than for the entire circuit. These unique blocks of logic have been identified and test sets generated for them. The approach employed for testing was to use pseudo-exhaustive test vectors whenever feasible. That is, each cone of logid is tested exhaustively. Using this approach, no detailed logic design or fault model is required. All faults which modify the function of a block of combinational logic are detected, such as all irredundant single and multiple stuck-at faults

Hierarchical social modularity in gorillas

Modern human societies show hierarchical social modularity (HSM) in which lower-order social units like nuclear families are nested inside increasingly larger units. It has been argued that this HSM evolved independently and after the chimpanzee–human split due to greater recognition of, and bonding between, dispersed kin. We used network modularity analysis and hierarchical clustering to quantify community structure within two western lowland gorilla populations. In both communities, we detected two hierarchically nested tiers of social structure which have not been previously quantified. Both tiers map closely to human social tiers. Genetic data from one population suggested that, as in humans, social unit membership was kin structured. The sizes of gorilla social units also showed the kind of consistent scaling ratio between social tiers observed in humans, baboons, toothed whales, and elephants. These results indicate that the hierarchical social organization observed in humans may have evolved far earlier than previously asserted and may not be a product of the social brain evolution unique to the hominin lineage

Measure for the Degree of Non-Markovian Behavior of Quantum Processes in Open Systems

We construct a general measure for the degree of non-Markovian behavior in open quantum systems. This measure is based on the trace distance which quantifies the distinguishability of quantum states. It represents a functional of the dynamical map describing the time evolution of physical states, and can be interpreted in terms of the information flow between the open system and its environment. The measure takes on nonzero values whenever there is a flow of information from the environment back to the open system, which is the key feature of non-Markovian dynamics.Comment: 4 pages, 2 figures, published versio

Witness for initial system-environment correlations in open system dynamics

We study the evolution of a general open quantum system when the system and its environment are initially correlated. We show that the trace distance between two states of the open system can increase above its initial value, and derive tight upper bounds for the growth of the distinguishability of open system states. This represents a generalization of the contraction property of quantum dynamical maps. The obtained inequalities can be interpreted in terms of the exchange of information between the system and the environment, and lead to a witness for system-environment correlations which can be determined through measurements on the open system alone.Comment: 4 pages, 1 figur

Quantum Equilibration under Constraints and Transport Balance

For open quantum systems coupled to a thermal bath at inverse temperature $\beta$, it is well known that under the Born-, Markov-, and secular approximations the system density matrix will approach the thermal Gibbs state with the bath inverse temperature $\beta$. We generalize this to systems where there exists a conserved quantity (e.g., the total particle number), where for a bath characterized by inverse temperature $\beta$ and chemical potential $\mu$ we find equilibration of both temperature and chemical potential. For couplings to multiple baths held at different temperatures and different chemical potentials, we identify a class of systems that equilibrates according to a single hypothetical average but in general non-thermal bath, which may be exploited to generate desired non-thermal states. Under special circumstances the stationary state may be again be described by a unique Boltzmann factor. These results are illustrated by several examples.Comment: 8 pages, 1 figure, leaner presentation, to appear in PR

Phenomenological memory-kernel master equations and time-dependent Markovian processes

Do phenomenological master equations with memory kernel always describe a non-Markovian quantum dynamics characterized by reverse flow of information? Is the integration over the past states of the system an unmistakable signature of non-Markovianity? We show by a counterexample that this is not always the case. We consider two commonly used phenomenological integro-differential master equations describing the dynamics of a spin 1/2 in a thermal bath. By using a recently introduced measure to quantify non-Markovianity [H.-P. Breuer, E.-M. Laine, and J. Piilo, Phys. Rev. Lett. 103, 210401 (2009)] we demonstrate that as far as the equations retain their physical sense, the key feature of non-Markovian behavior does not appear in the considered memory kernel master equations. Namely, there is no reverse flow of information from the environment to the open system. Therefore, the assumption that the integration over a memory kernel always leads to a non-Markovian dynamics turns out to be vulnerable to phenomenological approximations. Instead, the considered phenomenological equations are able to describe time-dependent and uni-directional information flow from the system to the reservoir associated to time-dependent Markovian processes.Comment: 5 pages, no figure

How large are present-day heat flux variations across the surface of Mars?

©2016. American Geophysical UnionThe first in situ Martian heat flux measurement to be carried out by the InSight Discovery‐class mission will provide an important baseline to constrain the present‐day heat budget of the planet and, in turn, the thermochemical evolution of its interior. In this study, we estimate the magnitude of surface heat flux heterogeneities in order to assess how the heat flux at the InSight landing site relates to the average heat flux of Mars. To this end, we model the thermal evolution of Mars in a 3‐D spherical geometry and investigate the resulting surface spatial variations of heat flux at the present day. Our models assume a fixed crust with a variable thickness as inferred from gravity and topography data and with radiogenic heat sources as obtained from gamma ray measurements of the surface. We test several mantle parameters and show that the present‐day surface heat flux pattern is dominated by the imposed crustal structure. The largest surface heat flux peak‐to peak variations lie between 17.2 and 49.9 mW m−2, with the highest values being associated with the occurrence of prominent mantle plumes. However, strong spatial variations introduced by such plumes remain narrowly confined to a few geographical regions and are unlikely to bias the InSight heat flux measurement. We estimated that the average surface heat flux varies between 23.2 and 27.3 mW m−2, while at the InSight location it lies between 18.8 and 24.2 mW m−2. In most models, elastic lithosphere thickness values exceed 250 km at the north pole, while the south pole values lie well above 110 km